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At the start of October, I went to see Elvis Costello at Town Hall, a small theater near Times Square with a history of hosting political meetings. You can see framed programs from some of those meetings, hazy, fading memories of the past, as you walk into the building:

The show had been loosely billed as a review of Elvis’s life and career, aligned with the memoir he released last summer, and I was looking forward to a few hours spent listening to him resculpting his songs in new and deeply satisfying ways. (I still felt warm from the time I saw him carry this off several years ago, at Carnegie Hall of all places, when he opened the show by playing the entire first side of My Aim is True, sang songs from all over the map, and told the kind of stories you might hear from the cool uncle you wish you had.)

For the first half hour, the show felt much like that night at Carnegie Hall. The stage was dominated by a giant TV, which showed 80’s Elvis videos as we waited for him to come on, then, once he did, ran a slide show of old family photos (hazy snapshots from the past again) and pictures from his early tours behind him as he played (solo, with acoustic guitar). He gave us both old and recent standards, culminating in a lovely rearrangement of Everyday I Write the Book. But as I burrowed deeper into my plush chair, getting comfortable for a couple more hours with Elvis’s fabulous songbook, he walked stage right, sat down at the piano, and smashed the time machine to bits.

In a halting, almost shattered voice, accompanied by the most austere, jagged piano figures you could imagine, he sang Shipbuilding, perhaps his greatest song. Written at the time of the Falklands war, Shipbuilding is a biography of out-of-work men in the English shipyards, waiting for the war to restart the shipyards and bring them jobs,

A new winter coat and shoes for the wifeAnd a bicycle on the boy’s birthday

and also for the warships that emerge from the shipyards to take those boys away, and bring them to their graves. “Is it worth it,” Elvis asks, and then asks again in a later verse that I hadn’t known before,

A small bunch of flowers is all that you get And a box to bury the baby

I had heard Elvis sing the song before, but not like this. I wish I knew how to describe the cocktail of regret and loss and compromise and inevitability I heard in his voice, but all I can do is point you to another song: if you listen to Springsteen’s Highway Patrolman, you’ll catch the same emotions when you hear Bruce’s voice trail off as he sings When it’s your brother, sometimes you look the other way at the end of the second verse. Hearing Elvis now, you could see shipyards, but also car factories on the outskirts of town, and mom and pop stores on Main Street, all of them filled with people’s dread of decisions they might know they’ll come to regret but still can’t avoid making. By the time the song’s resolution — diving for dear life, when we should be diving for pearls — exploded from the stage, you felt the full weight of the present day, of this election. Somehow, in just four minutes, Elvis had managed to make you feel the dilemmas of Trump voters deep down in your bones, more convincingly than any analysis I’ve read before or since the election. But he was only getting started.

He sang Deep Dark Truthful Mirror, an answer record in some ways, about facing up to the consequences of whatever choices you’ve made. Then, still at the piano, he started to tell us about a musical he was working on with the playwright Sarah Ruhl. It is an adaptation of the 1957 film A Face in the Crowd, which tells the story of the media-driven rise and fall of an American demagogue. If hearing Elvis sing Shipbuilding wasn’t enough to convince you he was addressing today’s political climate, the new songs he had written for the musical made it even plainer. He sang as the anti-hero, promising the angry and ignored to be their champion. He sang silly jingles that scoot back and forth across your screen and sell you silly things. And he sang for and with the faces in the crowd, all of us looking ourselves in the mirror and trying to find some common ground. The songs were theatrical, raw, maybe still works in progress — but they felt necessary and Elvis got them across. I am no fan of musicals, but I can’t wait to see what these songs will be like, and what they will mean, by the time they hit the stage, in the full blossoming of Trump’s America.

And then the finale. Given the range of Elvis’s songbook, it’s ironic that the song he is most associated with in the public imagination, What’s So Funny ‘Bout Peace, Love, and Understanding, is one he didn’t even write. But it is, and you won’t feel like you got your money’s worth unless you hear him play it, will you? Still, I’m not sure the song ever felt like it had more at stake than when Elvis sang it at Town Hall to close this show. And, as he sang it, the giant TV behind him projected a late 70’s, Armed Forces-era poster with the headline of the evening, Elvis’s answer to the America of Donald J. Trump, the next president of the United States: DON’T JOIN!

Soon it was over, and it was hard to believe we actually had to leave the building. But we did, and as I walked downstairs, the faded programs on the walls, from Town Meetings of long ago, were suddenly as sharp and timely as anything you might see on TV or on your Facebook feed. The past is not dead, not even past, as Faulkner said, and now all of us have many more town meetings to go to.

I have an 8:00 meeting this morning, so I’m going to take the early (6:36) bus in. I almost never go in this early, so to be safe, I am already downstairs putting on my shoes at 6:29. Sometimes I joke that I live so close to the bus stop that if I hear the bus from the second floor window of my house, I still catch it as it goes by. That’s an exaggeration, but not by much. Now I hear a sound outside that could be the bus, but I know it’s not, it’s never this early. Still, I peek out the door.

It’s the bus, already on the corner. Crap.

I dash out. The bus stop is diagonally across from my house, and fortunately, the bus is waiting at a red light. This gives me a chance: I run down to the corner and across the street with the light. Now the bus and I are facing each other, I wave, cross the other way when the light turns as the bus waits an extra couple seconds, and get on. I am feeling good about the world and my place in it.

Still, 6:29, that’s super-early. Unless maybe this is the previous bus, running super-late? I think I should say something to the driver. “Excuse me, which bus on the schedule is this?” It’s the morning, everything is rushed, who knows if I actually said “Excuse me.”

The bus driver, not one I’m familiar with, is not pleased. He barks at me: “It’s whatever bus it is when I get here!” I look behind him, see the bus is mostly empty. I know from experience that if it were the previous bus, running late, it would be overcrowded, so this must really be the 6:36. I give the driver my ticket and try to explain: you’re running way too early, people who count on this bus will miss it, then the next buses are overcrowded and run late, etc. I ask him to wait a few minutes to get back on schedule. He remains very hot, says (yells) that I better stop talking to him, threatens to call the police if I don’t get away from him. The good thing about him yelling at me is that the bus is still not moving. A couple people, breathless from running down the street, get on the bus while we’re going back and forth. I count this as a small victory.

A large man walks up the aisle from the back of the bus. I am hoping for a little support from a fellow commuter. “You better fucking stop talking to him so he can go!” he yells at me. “You’re holding the bus up! He’s going to call the cops!” This guy looks like he’d like nothing better than to slug me. “He’s calling the cops!” The bus driver is not calling the cops. My fellow passenger, though he is louder than the driver, does not actually take a swing at me. I sit down in one of the many empty seats.

The bus doesn’t move.

I take my book out of my bag and try to disappear into it. It is eerily silent. In moments of suspense, time feels suspended. The bus still doesn’t move.

Finally, after what must have been only a short wait but didn’t feel that way, the bus huffs and trundles forward. I check the time. It is exactly 6:36. We have been waiting for just a few minutes.

I mull things over as the bus heads into the city. I feel good that I managed to stay calm through the whole episode. Maybe this will be a good story to tell the children — the importance of keeping your cool. It occurs to me that the bus driver ended up doing exactly what I asked him to — waiting to leave until he was scheduled to, to the minute. Or was that just a coincidence? Something makes me decide to talk to him again, though I can’t tell exactly how or why I make that decision.

The bus pulls in to Port Authority. I am going to wait for everyone else to get off and then try to approach the driver. As the people ahead of me are getting off, I hear the usual end-of-trip courtesies: passengers say thank you, driver says you’re welcome or have a good day. That’s encouraging: this isn’t one of those guys who’s so nasty that people give up on saying thanks at the end of the ride.

Once is everyone else is off, I get off too. The driver is standing to the side. “Thanks for waiting a few minutes at the bus stop,” I say to him. “I wasn’t trying to pick a fight, I just…”

The driver is looking me in the eye. “Yeah, I know,” he says. “I get what you were saying.” I talk to him about the schedule, he says he understands, sometimes they get off schedule and it’s hard to keep track. We are talking to each other like people now. He says he’s sorry, and he seems totally sincere. I tell him my name, because that seems like a talking-like-people thing to do, and he tells me his. I was hoping to make peace, but this is more than I expected; in under a minute, our conversation has turned comfortably fraternal. I am feeling good about the world again as I head inside the bus terminal.

Now another man slides over to me. He is fiftyish, tall, thin, with slightly graying hair, wearing jeans and a blazer. “You know,” he says,”I saw the bus driver yelling at you, I got a video on my phone. I’m going to call the bus company.”

I don’t actually want him to call the bus company. I tell him that I just had a good talk with the driver, and that he seemed very direct and sincere. My companion isn’t impressed. “He’s just afraid for his job,” he says. He tells me that the driver has done this (I think he means run ahead of schedule) once before, that people were running for the bus and he didn’t care. He looks at me a little conspiratorially. “I think this guy just hates white people.”

Well. The driver, like the majority of bus drivers I encounter, is black. I am white. The guy I’m talking to now is white. The passenger who was yelling at me earlier is white. Most people on the bus are white, with a few exceptions. What is the logic here, how do you decide that a black man driving a bus full of mostly white people hates them because they’re white? Does the white man who came up to yell at me before hate white people too? Why do we look differently at angry black people than at angry white people?

The man I’m talking to is going his way and I’m going mine, and there isn’t time to ask these questions. But I as I walk up 8th Avenue on a sunny end-of-summer morning, I realize that I’ve lost the tidy story I was going to tell my kids about the virtues of keeping calm. And perhaps a bit of my confidence in those virtues as well.

The man sounds serious, that’s the first thing. Listen to Mick Ronson’s opening chord on Moonage Daydream, followed by the sound of Bowie’s voice coming in: “I’m an alligator,” he announces, in a grown-up voice that could credibly belong to, well, an alligator. There’s a little leather in it. You can’t help noting the parallel with how the Beatles start A Hard Day’s Night: a clear opening chord, a very brief pause, then a vocal that demands your attention. But while the Beatles emit unrestrained joy, the sound of the school doors swinging open at the start of summer vacation, an instant of anticipation before the bell rings and everyone rushes down the stairs into a world of vivid color, Bowie hits you in a worldlier way. You rush down the school steps, yes, but then your best friend’s older brother, the one who graduated three years ago, or was it four, grabs you, not roughly but with a force you can’t ignore, and pushes you up against the wall. Stand back here with me a minute, kid. Look around, take it all in, all of it. See what it’s really like out here. Serious stuff: even the moonlight in Bowie’s universe is serious. In Under Pressure, he sings of the terror of knowing what this world is about, and you can hear that terror across his work, from the very beginning all the way through to today. Listen to Space Oddity. Listen to Low (I’ve been breaking glass in your room again!). Listen to Ashes to Ashes. Listen, yes, to Blackstar.

Perhaps this is presumptuous, but I’m almost certain that you never knew until this past week how much you, and everyone else, loved Bowie. Within a day of hearing he was gone, I had established a routine. Every few hours, I would look for more tributes on Facebook: posts from friends, links to essays, appreciations from his fellow musicians, stories of chance encounters, all it resonating more than I had expected. The personal stories were genuinely moving, not corny. The musical appreciations were thoughtful and meaningful. Appreciating Bowie, appreciating each other for the shared feelings, appreciating the world more for having given rise to him, the communal mourning had a tangible sense of pride and purpose. All his children used it, all his children lost it, all his children boogied. It is plausible to think we will have a Best Bowie Tribute Pieces collection in bookstores by Christmas. And yet: his children? Really? Did he really mean so much, and why hadn’t we realized it before?

Bowie was always there, with that voice. When I first started listening to the radio, as a kid at the start of the 80’s, his entire 70’s output was in heavy rotation on every station in Boston I would tune to. Those were rock stations that played everything: oldies and classic rock (50’s and 60’s), punk and new wave, heavy metal, prog rock, singer-songwriters, soul, R&B, early rap, comedy records… and Bowie, a genre unto himself, and yet somehow connected to them all. Boys keep swinging all over in their musical tastes, with one artist or another thrilling you in any given week, but you always knew Bowie was outside all of that, more solid than the rest. He might sing about a brand new dance, but he never was one.

It’s surprising in a way that Bowie never seemed trendy, because he worked across such a range of musical styles. But what he achieved, more than any artist I know, is a genuine synthesis of all the types of music he touched. Somehow, you were always aware of the whole picture. Even the Beatles never quite managed that trick: in the moment when A Day in the Life was enveloping you, you weren’t harking back to It Won’t be Long. But somehow when you heard Let’s Dance, you were still conscious somehow of Young Americans, and Rebel Rebel, and Ziggy Stardust too. I still don’t know how he did that. Music is so powerful emotionally that it’s supposed to be reductive: you know a song really works when it makes you believe, in the moment when you hear it, that the song, just the notes you’re hearing, right here, right now, is the only thing that matters. Bowie’s special talent was that he could pack so much into that moment. It was his range, yes, but also his genius for synthesis and encapsulation. When you heard a Bowie song, and felt that this is all that matters, what you understood by this was especially rich.

The lyrical content of those moments mattered just as much as the music. Bowie was broader than the rest here too: he covered more themes than the other artists on the radio. When you listened to him, you heard about space, you heard about Nixon, you heard about the Berlin wall, and you heard about love and loss and yearning too, and time and mortality and death. I think many of us, discovering him on the cusp of adulthood, wondering about our place in the world, a little alienated, maybe feeling we were too smart for our own good, found his universe and the people who populated it uncommonly attractive. You could imagine yourself in a Bowie song. Synthesis again, lyrically this time, bringing the whole world into the moment.

I think this is why so many of the tributes to Bowie that I’ve seen this week treat him, with an unusual lack of self-consciousness, as an authority figure. Even a generation that rejected authority, that mistrusted its parents and political leaders and social institutions, needed a trail guide to its surroundings. For many of us, whether we thought of ourselves as artistic or not, Bowie was our ranger, a self-made cultural Buddha, an older brother who could guide us and shield us at the same time. Reading the tributes to Bowie from other musicians, all genuine and heartfelt, I’m reminded of Picasso speaking of Cezanne as his one and only master, the father of us all. Perhaps Bowie was like Picasso in a way, using and mastering multiple artistic styles, but he was even more like Cezanne, endowing his art with new gravity and inspiring generations, not to copy him but to make their own art. Seriousness again, from his voice to his musical explorations to the range of his lyrical themes.

Bowie used that authority in his work, too. It is remarkable, given his level of artistry and artfulness, how plainly, how directly he could address his audience. Listen to the lyrics of Rock and Roll Suicide: the knives seem to lacerate your brain? I’ve had my share, I’ll help you with the pain! You’re not alone, turn on with me! This is a man who knows he has followers, who accepts the responsibility, who knows what he can say to them. The words look overwrought and pretentious on the page, but they work in the song, Bowie knows exactly what he can get across and how. He is a fully aware Buddha, not an accidental one.

You find Bowie’s influences all over the place, where you expect them and where you don’t. I went for a run in the park the other morning, with a collection of his 70’s songs on my phone as company. Toward the end, Ashes to Ashes came on, with its final chant: my mama said, to get things done, you better not mess with Major Tom. Involuntarily, my mind pulled up Bowie’s other use of that phrase — get things done — in Modern Love (I don’t wanna go out / I wanna stay in / Get things done), and then pivoted to work, thinking about people I work with, who gets things done and who doesn’t. I realized, then, that the phrase in the song represents a core value that has been central to my entire work life, that my definition of effectiveness, in myself and others, is framed in terms of getting things done. It would be a gross overstatement to say that’s because of Bowie, of course. But it doesn’t seem entirely independent of him, either.

Thinking about Bowie on my run, I remembered too how in the early days of email, you would mostly send them to friends, and you would try to make them witty and artful. One favorite trick to add erudition, or other attitude, was to quote song lyrics, sometimes in context, sometimes as complete non sequiturs. Don’t lean on me man because you can’t afford the ticket. Bowie lines were great for that, which made this tribute from Brian Eno especially poignant. It turns out that our heroes Bowie and Eno, collaborators for decades, communicated in exactly the same way we did, only they didn’t need to lift their witty lines from Bowie and Eno. Turn over any rock this week, and you find Bowie’s influence.

Of course, that influence was only possible because he made beautiful art. Bowie’s voice has an older brother’s authority, but when he sent it to the upper register — think of the octave-high, over-the-rainbow jump in the chorus of Starman, all of Ashes to Ashes, and several songs on Blackstar (especially Dollar Days and the title track) — it also has a beauty that you rarely hear in rock and roll. Forgive me for always coming back to the Beatles, but when I think of Bowie singing in the upper register, I can’t help thinking of John Lennon, Bowie’s own older brother, singing at the end of “God,” on his first solo record. “I wa-a-s the dreamweaver,” John sings, “but no-o-w I’m reborn.” It is the most beautiful and affecting vocal I know in popular music, and Bowie sings in that rarefied neighborhood too. The voice of God, in more ways than one. I think Henry Rollins is spot on in his Bowie tribute when he speaks of him as having an “intimate distance” with his audience. The distance of his authority, the intimacy of his beauty, the two always intertwined.

I posted next to nothing here in the second half of last year, so here’s making up for lost time: here is a list of a few notable things I ran across over that period. I can’t resist stealing the format Greil Marcus uses for his monthly Real Life Rock Top 10 column, especially since he just published a book collecting all the columns he’s written over the years. Something to strive for.

1. Laurie Anderson, Heart of a Dog. In a year of decent-to-good memoirs by good-to-great musicians, this 80-minute meditation on memory, time, and loss was more powerful than the rest of them put together. There is a lot to say about this multilayered film, but two pieces in particular, one in the middle and one at the end, and neither one about dogs, truly blew me away. It would ruin the movie to give them away, but in the first, “A Story About a Story,” the artist, who’s been telling personal stories in one form or another for forty years, is brave enough to unpack and expose all the assumptions and poses behind the whole genre. And in the second, “The Lake,” she gives you a take on parent-child dynamics that my wife and I are still arguing about. Anderson’s work is always artistic and creative, but this film has an emotional rawness and a directness that feels like a brand new direction more than a summation. She was kind enough to stop by to chat at the screening that I attended, and I asked her if the “story about a story” episode in the middle of the film was indicative of a new outlook on storytelling as a whole. She said yes, in a way that made me think she was still figuring out the consequences, and that they would flow into her work for years to come. I can’t wait.

2. Mourning Sun, at the West End Theatre, NYC. Directed by my friend Ari Laura Kreith, this is a play about the fallout from the cycle of child marriage, rape, and pregnancy in Africa. You worry that an issue play might be didactic or artless, but there is a lot here that is artful, especially a scene late in the first act that brings the issue home in the most devastating terms.

You see a stark set on an almost bare stage, you see a young woman getting on a bus. The bus driver notices she smells like a bathroom, the woman explains it away: she just encountered someone incontinent, she says. She moves, unsteadily, to the back of the bus. The passengers around her rise up in disgust, the driver kicks her off the bus. She tries to get on another bus, and the cycle repeats. The woman has an obstetric fistula, a hole in her bladder, from when she was raped as a child bride, became pregnant, and went into prolonged labor that her body wasn’t mature enough to handle. Now she can’t stop peeing. She tries to get on a third bus, repeating the same painful dialogue, and by then you’re squirming in your seat, so uncomfortable that you think you might actually smell the urine in the theater.

3. Richard Thompson, “Fergus Lang.” I saw Richard Thompson play a great solo acoustic show at NJPAC in Newark in April, and the one new song that stayed with me was this caustic takedown of a not-at-all disguised Donald Trump figure. It was springtime then, months before Trump announced for president, and Thompson’s satire played mostly for laughs. “Fergus Lang (the Trump stand-in) has a fine head of hair,” Thompson sang in the chorus, “when the wind’s in the right direction.” In the moment, the song seemed totally over the top — but something changed later in the year, as Trump became the 2015 king of all media and the frontrunner for the Republican nomination. When you hear “Fergus Lang” now, all you can do is shake your head that it doesn’t go nearly far enough. Thompson may have a rich artistic imagination, but the real Fergus Lang has managed to imagine a kind of politics that even Thompson couldn’t dream up. If art is the expression of imagination, as Henry Moore said, then is Donald Trump also the frontrunner for the Grammy for New Artist of the Year?

4. Golden State Warriors and Kansas City Royals. Sports stories don’t have to be inspirational, and the good guys don’t always end up on top. But when the teams that play with the most joy end up winning it all, it’s beautiful to watch.

5. The Red Iguana, Salt Lake City, UT. Mexican is my comfort food, and this unassuming place in Salt Lake City had the best mole sauces, and probably the best Mexican food, that I’ve ever eaten. When you first come in, they give you a sample of eight moles, and you can have your meal made with any of them. I had a chile relleno with a combination of two sauces, and I still feel like I can taste them months later. I can’t imagine anything hitting the spot more after a long day’s drive across Utah.

6. The Mekons, “Heaven and Back,” Bowery Ballroom, NYC. After a recent documentary expanded their cultural presence from hundreds of fans to possibly thousands, the Mekons toured this summer to larger crowds than usual, and on this night in July, the Bowery was packed. The band responded with fierce intensity, cutting out much of the usual banter between songs, and reminding you that no matter what you knew or thought you knew about them, they were a great rock and roll band first. They even brought out the high leg kicks for “Heaven and Back”… and then Rico fell backwards into Jon’s guitar amp, some of the sound went out, and the song disintegrated into three minutes of archetypal inter-Mekon insults, sarcasm, and laughter. Hard as they may try, they can’t escape being hilarious. Then everybody picked themselves up and tore into the next number. It was as perfectly Mekonic as you can get.

7. Sleater-Kinney, “Was it a Lie,” Kings Theatre, NYC. The opening notes echoed the better-known “Jumpers,” S-K’s other death-themed song, which the band had ripped through near the beginning of the set. But while “Jumpers” stands in direct opposition to its subject matter, as perhaps the most life-affirming song you’ll ever hear, “Was it a Lie” is a lot harder to pin down. It is complex, and subtle, and what makes it work is the astonishing delicacy and empathy of Corin Tucker’s vocal. This one is for everyone who makes the mistake of thinking of Tucker mainly as a screamer.

8. Sleater-Kinney, “Merry Christmas (I Don’t Want to Fight Tonight),” Kings Theater, NYC. One of the band’s few false moves on this December night was a rushed rendition of one of their early statement cuts, “I Wanna Be Your Joey Ramone.” It didn’t ring true because it came across like a standard rock number, without any of the mystery, emotion, and slow self-discovery of the original version. The otherworldly shrieks that began the chorus were reduced to simple yells, the band calling happily to their audience, no longer the involuntary sounds of a woman alone in a room, discovering, step by step, the power of her voice. The song didn’t seem relevant for the band anymore.

Then, when the band came back out for their encore, Carrie announced, “We know it’s Hanukkah,” (and indeed a menorah rested on top of her amp), “but we’re going to play a Christmas song.”

What came next turned out to be a slightly obscure mid-period piece by those same Ramones. If you’ve never heard it, that’s because it’s not that notable: the original is hedged, campy, and plays largely for laughs. But S-K changed the terms of the song. Carrie put down her guitar, caressed the mic and slithered over the stage just like Joey Ramone used to, but with a seriousness of purpose that was all Sleater-Kinney. When she wished you “Merry, merry, MERRY Christmas,” she held you by the scruff of your neck; when she called out, “I don’t want to fight tonight!” her voice was filled with desperation, but also a keen awareness of her own capability. It was crystal clear, in that moment, why “I Wanna Be Your Joey Ramone” had sounded obsolete earlier: the band was already your Joey Ramone, and much, much more.

Meanwhile, alone in a small town basement somewhere, a thin, quiet, completely straight-eyed 14-year old was trying out voices that she might use to let you know how much she wanted to be your Corin Tucker, Carrie Brownstein, and Janet Fucking Weiss. Shoulders of giants.

9. Mad Max: Fury Road and Star Wars: The Force Awakens. Two sequels to beloved sci-fi trilogies from the late 70’s and early 80’s with more than a few parallels. Both series were known for a grimier than usual picture of the universe, for one thing, and in both cases the second film in the trilogy was clearly the best and the third was relatively weak, for another. (In one case there was also a set of prequels that nobody wants to talk about, so I won’t either.) Seeing the Star Wars film was like seeing a band you used to like as a kid getting back together after twenty years and delivering a crowd-pleasing show of their hits, all the old formulas working as well as ever. Which might seem like enough, until you see Sleater-Kinney, or Fury Road.

10. Lou Reed, “Turning Time Around.”A late 90’s composition by Laurie Anderson’s late husband, played over the closing credits of Heart of a Dog, fitting the moment so perfectly that you couldn’t believe it wasn’t written specifically for the movie. Weren’t Lou and Laurie in the studio together working on it, going over sounds and timing and exactly how the credits would roll over the track?

Don’t look for the start of spring in the calendar. You can’t predict ahead of time when it’ll come, yet you always know it on the day, when something makes you rush outside without bundling up first, and once you’re out, you start inventing reasons to stay out longer, not reasons to come back in.

This year the start of spring came on a Sunday, about a week after the official date. The snow had mostly melted a couple weeks earlier, and the temperature was rising steadily through the early afternoon. My sons and I decided we needed to give the local ball field a try. It can’t be that muddy, can it? We took our baseball things — bat, gloves, and balls — and headed over.

It wasn’t muddy at all, and more than warm enough to play. We tossed a ball around to warm up, then took our regular spots — me pitching, one boy batting, the other catching. Despite the winter layoff, they remembered what to do, where to stand, how to swing. Within a few minutes they were as comfortable with their new metal bat as they had been with a wiffle bat by the end of last summer. They swung and missed often, but got their share of hits too, a few balls going past the infield, boys running happily around the bases when they made contact. It must have looked fun, because pretty soon other kids started wandering over to play. A friend from the school bus, two chatty third graders we didn’t know but who soon seemed like old friends, one quiet boy who knew to take over catching when my sons wanted to go out in the field, still another who was too shy to ask but looked like he really wanted to play.

A batting order was formed. After a couple cycles through it, my younger son announced he wanted to pitch. I was skeptical — but OK, sure, give it a shot. We agreed on how far he should stand from the plate, and he started firing balls in. I stood over to the side and watched. He was no worse at getting the ball over the plate than I had been, and the batting rotation went on — swings, misses, balls hit up the middle, balls hit straight up in the air. Everyone knew to run when they hit the ball. Boys who weren’t up to bat stood out in the field, chased balls, tried to throw to each other, to tag the runner — without much grace, for now. Out here, in the developmental leagues of Montclair, NJ, it’s very much a hitter’s world.

No longer needed in the game, I could look around, taking in the whole park — the field, the pond to my right, the playground to my left. We have been regulars since we moved to town, almost seven years ago now, when the first boy was just a year old and the second was just a plan. How many times have we celebrated the first day of spring here? Around this time two years ago, my older son was in kindergarten, and we came out on a sunny day to find that all his friends from school were at the park too. The kids ran off to play, the parents stood and chatted, everyone happy to see each other, and suddenly my embarrassing suburban fantasy, of a real community and life lived at a sustainable pace, crystallized into something real and true. And then last year, we came here on a similar day, expecting more of the same, only the kids got bored at the playground after half an hour, and went off to join another set of kids playing baseball on the field. They’d never played before, didn’t know what to do, couldn’t hit the ball, and left in frustration, which led directly to a summer’s baseball education through backyard wiffle ball games. And now here we were a year later, starting up a game of our own, pulling in other kids. Oh what Proust could have done with a playground and a ball field.

In the actual day, time passed in a more humdrum manner. First one kid got called home by his parents, then another, and finally it was just the three of us on the field again. I went back to pitching. More time went by, and we all started to drag a bit. I would miss the plate more often than not, and when I did get the ball over, the boys didn’t put level swings on it, and hardly connected any more. Time to go.

We walked over toward the car. I carried the bat, the boys carried gloves and balls. We bumped fists, patted shoulders and backs, complimented each other, and meant it: Good game. And as we walked, I went back even further in time, to pre-parent days, evening endings to long afternoon frisbee games when I was still a student, walking off the field with friends, sweaty and exhausted, arms and legs sore, barely able to see in the approaching darkness. Good game. My sons and I walked off the ball field together, side by side, and it felt like the first day, not just of spring, but of something else too.

“As long as the music is playing, you’ve got to get up and dance. We’re still dancing.” These words were spoken by Citigroup CEO Charles Prince in July 2007, shortly before the start of the financial crisis. He was talking about Citi continuing to lend and lend (especially for the sake of financing leveraged buyouts) in spite of fears that reduced liquidity (coming, for example, from much lower valuations of subprime securities and other securities on Citi’s balance sheet) would leave the bank significantly exposed.

Prince would eventually be derided both for his stewardship of Citi and for his commentary on dancing, which became a summation of the financial sector’s attitudes and behavior leading up to the crisis. But as an observation of social myopia, his words seem pretty spot-on. When we start to see a future crisis looming, we usually realize, on some level, that we’ll need to adjust our day-to-day behavior to prepare for the storm, or to head it off — to trade short term gratification (making money, having fun, whatever) for long-term sustainability. The question is when. When we’re by ourselves, making decisions independently, we usually do a decent job of timing the shift. If you find out that your roof is starting to leak, you’ll probably fix it before water floods your house. But when we’re in large groups, we’re guided by the behavior of others. And if we don’t see anyone else preparing for the crisis, most of us are reluctant to be the first ones to act.

If I were a better person, I would keep Prince in mind every time I hear (almost daily, now) about irreversible climate change, the most obvious and important example of a looming crisis that we’re collectively ignoring. But apparently I am still too myopic for that. Instead, his words occurred to me yesterday as I thought about the Super Bowl. At this point, we’re all aware that football, as currently played, sometimes results in repeated concussions, brain injury, and shortened lifespans — that, when we watch a game, we might literally be watching some of the players, perhaps even the very best ones, killing themselves out there. Already, many parents are discouraging or forbidding their kids from playing. You might think that, with the game heading for what feels like a long-term crisis, perhaps starting to lose its moral acceptability, there might be less business as usual — that some of us would look to the future and stop watching.

But — the Super Bowl feels like an important shared experience. And sometimes it’s really fun. For now the music is still playing, and we’re still dancing.

Doing math in school is usually about getting an answer. Doesn’t matter if you’re multiplying 3-digit numbers, integrating by parts, figuring out what happens when a train leaves Chicago at 6 AM, or counting paths through a maze. Doesn’t matter if you’re in grade school or high school, math class or math team. Problem. Answer. Find out if your answer was right. On to the next problem.

It’s a shame, because the first time I really thought hard about math was when this paradigm blew up. It happened around seventh grade, when we were learning how to convert repeating decimals into fractions. We had done a few standard problems (converting, say, 0.333… into 1/3, or maybe 0.424242… into 42/99, simplified to 14/33), when along came 0.999… Which, if you used the standard method (multiply by a power of 10, subtract the original from the result to cancel the infinitely repeating part, solve for the original), appeared to be equal to 1. And that was an answer I wasn’t remotely ready to accept.

Point (me): That couldn’t be right, because we started with 0-point-something, which is clearly less than 1.

Counterpoint (teacher): OK, but you had no problem turning 0.333… into 1/3, and we’re just repeating the same method when we turn 0.999… into 1.

Point: But I can turn 1/3 back into 0.333… by dividing 1 by 3, and I can’t turn 1 into 0.999… by dividing 1 by 1.

Counterpoint: You can. It’s just a funky kind of long division, with a remainder of 1 each time. At the first step, you’re dividing 1 by 1, and you say the answer is 0, remainder 1. From then on, you’re dividing 10 by 1, and you say the answer is 9, remainder 1, over and over again.

Point: That’s against the rules, the remainder has to be less than what you divide by!

Counterpoint: If you agree that 0.333… = 1/3, just multiply both sides by 3 and see what you get.

Point: But the decimal expansion of 1 is 1.000…! How can it have another one?

Back and forth we went (did I mention that I loved to argue?). It wasn’t question and answer anymore, but questions spawning questions. Was it really OK to say 10 times 0.999… was 9.999…, or were we pulling some strange extra little bit from infinity? It did look OK to multiply 0.333… by 10, but was that somehow suspect too? What was really going on out there at infinity, and what did it mean to be just a tiny smidgen less than 1? What were the real rules of long division, anyway?

For the first time, math seemed very open, up for grabs. My seventh grade mind wasn’t even sure what the answers to these questions could look like. My teachers said there were these things called limits, which helped you represent what happens out at infinity. So 0.999… wasn’t an ordinary number, it was a limit, but it was equal to 1, which was an ordinary number. My head spun. Eventually I declared that anything with infinitely repeating 9’s was undefined and called it a day. (That was right in a way: nobody defines infinite sums carefully in grade school, although I wouldn’t have said that, say, 0.333… was undefined too.) And everyone went back to the usual routine. Problem. Answer. On to the next problem.

But several aspects of the experience stayed with me to this day:

1. An expanded sense of what a math question could be, and what you could learn from it. Once in a while, you’ll hear kids complain about not understanding what a math problem means, or what it’s asking them to do. More frequently, at least these days, the parents are the ones complaining (and much more loudly, too). Often they’re right: hundreds of poorly written math problems get sent home every day. But sometimes it’s through trying to make sense of a question, whether someone else’s or your own, that you learn the most. Does 1 – 0.999… = 0?Why or why not? These were questions of a different kind, as far as you could get from the land of how many more marbles does Dorothy have than Fred. Behind the scenes, infinity was revealing itself, as the subject matter (where 0.999… finally reached 1, or didn’t), and also as the true scope of math. It was thrilling.

2. Years later, when I finally got to learn about limits, I paid a lot of attention. I’d been promised that they would resolve the mystery, and they did! Short summary in case you haven’t studied this stuff: the idea is that when you write down 0.999…, or any other decimal that doesn’t terminate, the dots mean that you’re not writing down an ordinary number in the literal sense. Instead, 0.999… is shorthand for a sequence of numbers (here 0.9, 0.99, 0.999, 0.9999, and so on), defined by some rule that pins down exactly what “and so on” means. (In this case, the rule is that you get the n-th element of the sequence by adding 9/(10n) to the n — 1-st element. For example, you start with 9/10 as the first element, add 9/100 to get the second, then add 9/1000 more to get the third.) Out at infinity, this sequence converges (gets arbitrarily close) to 1, meaning that you can’t squeeze any other number between 0.999… and 1. Once you have convergence, limit theory tells you that the arithmetic manipulations are OK: you’re allowed to write 3×0.333… = 0.999…, 10×0.999… = 9.999…, and so on. There’s a lot more to say here, and this wonderfully detailed yet accessible article by Jordan Ellenberg is very insightful on both the math and the underlying intuition.

It was amazing to me to learn all this. Back in seventh grade, I had gone from some ordinary-looking manipulations of sums and products to a set of questions that felt like philosophy, and now here was math providing real answers to those questions, on its own terms, putting me back on firm ground. In their way, the answers were as mind-expanding as the questions had been. How cool was that?

3. Speaking of those ordinary-looking manipulations, I would never naively trust them again. Maybe your eyes glazed over when you first encountered proofs in math class: why bother proving things that seem out-and-out obvious? But for me, after seventh grade, the obvious could be questionable (like those algebraic manipulations that led to such a weird outcome) or flat-out false (a single number really could have two separate decimal expansions). So when I finally got to proofs in school, I couldn’t have been happier. You mean you can actually prove it? You can carefully work through the all moving parts and identify the statements and methods that you can genuinely trust and use? Bring it on!

4. Faith in the long view. Once I heard someone say that math has two-minute problems, two-hour problems, two-day problems, two-month problems, and two-year problems. I wasn’t ready for multi-year territory as a seventh grader, already getting antsy after a couple weeks without a real answer. Being able to arrive at a satisfying solution eventually, years later, was a very big deal. For a long time afterwards, when I got stuck on a math problem, or on something else, I would recall how long it took to make sense of 0.999… And sometimes, with a little more work, a few hours or days or months later, I’d get unstuck. For what it’s worth, even this post took a few tries over a couple weeks to write.

So, kids, don’t be afraid of questions that might be a little unclear, or that don’t point you directly to an answer. And parents, don’t rush to ridicule that confusing math homework sheet on Facebook. Maybe a little confusion is part of the territory, and just means that you haven’t solved the problem yet. Not understanding can make you frustrated, but it can also mean you’re on the cusp of learning something. Or even that the learning is already underway.